Finite Group Databasebeta

← #26005174

Subgroups — #26005174

Order 11008.

7210 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148514C214yesmaximal, complemented
2#19148496C214yesmaximal, complemented
3#19148490C212yesmaximal, complemented
4#19148486C212yesmaximal, complemented
5#19148482C211yesmaximal, characteristic, complemented
6#19148481C211yesmaximal, characteristic, complemented
7#19148469C211yesmaximal, characteristic, complemented
8#19148452C214yesmaximal, complemented
9#19148439C214yesmaximal, complemented
10#19148422C218yesmaximal, complemented
11#19148194C214yesmaximal, complemented
12#19148191C214yesmaximal, complemented
13#19148146C218yesmaximal, complemented
14#19147979C214yesmaximal, complemented
15#19147926C212yesmaximal, complemented
16#19147890C214yesmaximal, complemented
17#533×D43C211yesmaximal, characteristic, complemented
18C2×#14583447C211yesmaximal, characteristic, complemented
19#19147793C212yesmaximal, complemented
20C4×#41×D43C211yesmaximal, characteristic, complemented
21C43×#3508C211yesmaximal, characteristic, complemented
22C22×#10621900C2212yes—
23C2×#41×D43C2211yescharacteristic
24#14583635C2218yescomplemented
25#14583635C2214yescomplemented
26#14583632C2218yescomplemented
27#14583628C2214yescomplemented
28#14583627C2214yescomplemented
29#14583622C2214yescomplemented
30#14583619C2214yescomplemented
31#14583619C2218yescomplemented
32#14583618C2218yescomplemented
33#14583618C2218yescomplemented
34#14583613C2218yescomplemented
35#14583608C2218yescomplemented
36#14583599C2218yescomplemented
37#14583596C2218yescomplemented
38#14583596C22116yescomplemented
39#14583594C22116yescomplemented
40#14583592C22116yescomplemented
41#14583591C2218yescomplemented
42#14583589C2218yescomplemented
43#14583586C22116yescomplemented
44#14583580C22116yescomplemented
45#14583575C22116yescomplemented
46#14583569C2214yescomplemented
47#14583557C2218yescomplemented
48#14583556C2218yescomplemented
49#14583548C2218yescomplemented
50#14583543C2218yescomplemented
51#14583516C2218yescomplemented
52#14583514C2218yescomplemented
53#14583512C2214yescomplemented
54#14583511C2214yescomplemented
55#14583503C2214yescomplemented
56#14583492C22116yescomplemented
57#14583481C22116yescomplemented
58#14583478C2218yescomplemented
59#14583475C2212yes—
60#14583470C2212yes—
61#14583469C2214yescomplemented
62#14583466C2212yes—
63#14583462C2214yescomplemented
64#14583459C2218yes—
65#14583456C2211yescharacteristic, complemented
66#14583456C2214yescomplemented
67#14583455C2212yescomplemented
68#14583454C2212yescomplemented
69#14583454C2214yescomplemented
70#14583453C2214yescomplemented
71#14583452C2212yescomplemented
72#14583451C2214yescomplemented
73#14583448C2214yescomplemented
74#14583447C2212yes—
75#14583447C2214yes—
76#14583447C2212yes—
77#14583447C2214yescomplemented
78#14583447C2212yescomplemented
79#14583447C2212yescomplemented
80#14583447C2214yescomplemented
81#14583447C2214yescomplemented
82C2×#13063325C2211yescharacteristic, complemented
83C4⋊Q8×D43C2212yescomplemented
84#14583431C2218yescomplemented
85#14583431C2218yescomplemented
86#14583430C2218yescomplemented
87#14583430C2218yescomplemented
88#14583430C22116yescomplemented
89#14583428C2218yescomplemented
90#14583428C2218yescomplemented
91#14583426C22116yescomplemented
92#125×D43C2212yescomplemented
93C2×#13063312C2212yescomplemented
94#14583409C2218yescomplemented
95#14583409C2218yescomplemented
96#14583406C2218yescomplemented
97#14583405C2218yes—
98C22⋊Q8×D43C2214yes—
99C2×#13063296C2214yes—
100#14583378C2218yescomplemented
101#14583378C2218yescomplemented
102#14583376C2212yescomplemented
103#14583376C2212yescomplemented
104#14583374C2212yescomplemented
105#14583372C2218yes—
106#41×Dic43C2211yescharacteristic
107#41×Dic43C2218yescomplemented
108C4×#10621902C2212yescomplemented
109C4×#10621898C2211yescharacteristic
110C4×#10621898C2212yescomplemented
111#14583367C2211yescharacteristic
112#14583367C2212yescomplemented
113C4×#10621900C2214yes—
114C4×#10621900C2218yescomplemented
115C4×#10621900C2218yescomplemented
116C4×#10621900C2218yescomplemented
117C4×#10621900C2212yescomplemented
118C4×Q8×D43C2214yescomplemented
119C4×Q8×D43C2212yescomplemented
120C2×D4×Dic43C2214yescomplemented
121C4×D4×D43C2214yes—
122C4×D4×D43C2212yescomplemented
123C2×#13063281C2218yescomplemented
124#117×D43C2211yescharacteristic
125#117×D43C2212yes—
126#117×D43C2212yescomplemented
127C2×C42×D43C2211yescharacteristic
128C2×C42×D43C2212yescomplemented
129C43×#559C2214yescomplemented
130C43×#550C2214yescomplemented
131C43×#546C2218yescomplemented
132C43×#540C2214yescomplemented
133C43×#535C2212yes—
134C43×#533C2211yescharacteristic, complemented
135C43×#532C2214yescomplemented
136C2×#127×C43C2211yescharacteristic, complemented
137C43×#518C2212yescomplemented
138C4×#41×C43C2211yescharacteristic
139C2×#10621902C2311yescharacteristic
140C2×#10621898C2311yescharacteristic
141C2×#10621898C2312yes—
142C2×#10621900—216no—
143C2×#10621900C2312yes—
144C2×#10621900C2314yes—
145C2×#10621900C2311yescharacteristic
146C2×#10621900C2314yes—
147C2×#10621900C2314yes—
148C2×#10621900C2314yes—
149C2×#10621900C2318yes—
150#41×D43—28no—
151C22×Dic86C2312yes—
152C2×Q8×D43C2311yescharacteristic
153C2×Q8×D43C2314yes—
154C22×C22⋊D43C2314yes—
155C2×D4×D43C2312yes—
156C2×D4×D43C2311yescharacteristic
157C23×Dic43C2314yes—
158C22×C4×D43C2312yes—
159C22×C4×D43C2312yes—
160C22×C4×D43C2314yes—
161C22×C4×D43C2311yescharacteristic
162#13063325C2314yes—
163#13063325C2314yes—
164#13063325C2312yes—
165#13063325C2312yes—
166#13063325C2312yes—
167#13063324C2314yes—
168#13063324C2314yes—
169#13063323C2314yes—
170#13063323C2314yes—
171#13063321C2314yes—
172#13063320C23116yes—
173#13063318C23116yes—
174#13063318C23116yes—
175#13063318C23116yes—
176#13063318C23116yes—
177#13063318C23116yes—
178#13063317C2318yes—
179#13063317C2312yes—
180#13063316C23116yes—
181#13063316C2318yes—
182#13063316C2314yes—
183#13063315C2318yes—
184#13063315C23116yes—
185#13063313C2314yes—
186#13063312C23116yes—
187#13063312C2318yes—
188#13063312C2318yes—
189#13063312C2314yes—
190#13063312C2314yes—
191#13063312C2314yes—
192#13063312C2314yes—
193#13063311C23116yes—
194#13063309C2318yes—
195#13063308C23116yes—
196#13063307C23116yes—
197#13063307C23116yes—
198#13063306C2318yes—
199#13063306C23116yes—
200#13063306C23116yes—
201#13063306C23116yes—
202#13063305C2314yes—
203#13063305C2318yes—
204#13063304C23116yes—
205#13063304C2318yes—
206#13063304C2314yes—
207#13063304C2318yes—
208#13063303C2318yes—
209#13063302C23116yes—
210#13063302C2318yes—
211#13063302C23116yes—
212#13063301C2318yes—
213#13063301C2314yes—
214#13063298C23116yes—
215#13063297C23116yes—
216#13063297C23116yes—
217#13063296C2318yes—
218#13063296C23116yes—
219#13063296C2318yes—
220#13063296C2318yes—
221#13063296C2318yes—
222#13063296C2318yes—
223#13063296C2318yes—
224#13063294C2318yes—
225#13063293C23116yes—
226Q8×Dic43C2318yes—
227Q8×Dic43C2312yes—
228Q8×Dic43C2314yes—
229C4×Dic86C2318yes—
230C4×Dic86C2314yes—
231C4×Dic86C2314yes—
232C4×Dic86C2318yes—
233C4×Dic86C2312yes—
234C4×Dic86C2318yes—
235C4×Dic86C2318yes—
236#13063290C2314yes—
237#13063290C2312yes—
238#13063290C2314yes—
239#13063290C2318yes—
240#13063290C2318yes—
241#13063290C2318yes—
242C4×D172C2314yes—
243C4×D172C2312yes—
244D4×Dic43C2318yes—
245D4×Dic43C2314yes—
246D4×Dic43C23116yes—
247D4×Dic43C2318yes—
248D4×Dic43C2318yes—
249D4×Dic43C2318yes—
250D4×Dic43C2312yes—
251D4×Dic43C2318yes—
252D4×Dic43C2318yes—
253D4×Dic43C2318yes—
254D4×Dic43C23116yes—
255#13063287C2314yes—
256#13063287C2312yes—
257C4×C22⋊D43C2314yes—
258C4×C22⋊D43C23116yes—
259C4×C22⋊D43C23116yes—
260C4×C22⋊D43C2314yes—
261C4×C22⋊D43C2314yes—
262C4×C22⋊D43C23116yes—
263(C22⋊D43)⋊C4C23116yes—
264(C22⋊D43)⋊C4C2314yes—
265(C22⋊D43)⋊C4C2314yes—
266(C22⋊D43)⋊C4C2314yes—
267(C22⋊D43)⋊C4C23116yes—
268(C22⋊D43)⋊C4C23116yes—
269#13063284C23116yes—
270#13063284C2318yes—
271#13063284C2311yescharacteristic
272#13063284C2312yes—
273#13063284C2312yes—
274#13063283C2318yes—
275#13063283C2312yes—
276#13063283C2314yes—
277#13063283C2314yes—
278#13063282C2312yes—
279#13063282C2314yes—
280#13063282C2312yes—
281#13063282C2312yes—
282#13063281C2318yes—
283#13063281C2318yes—
284#13063281C23116yes—
285#13063281C23116yes—
286#13063281C2312yes—
287#13063281C2314yes—
288#13063281C2314yes—
289#13063281C23116yes—
290C2×C4⋊Dic43C2314yes—
291C2×Dic43⋊C4C23116yes—
292C4⋊C4×D43C2318yes—
293C4⋊C4×D43C2314yes—
294C4⋊C4×D43C2312yes—
295C4⋊C4×D43C2314yes—
296C4⋊C4×D43C2314yes—
297C2×C22⋊Dic43C2318yes—
298C2×C22⋊Dic43C2318yes—
299C22⋊C4×D43C2312yes—
300C22⋊C4×D43C2314yes—
301C22⋊C4×D43C2314yes—
302C2×C4×Dic43C2312yes—
303C2×C4×Dic43C2311yescharacteristic
304C2×C4×Dic43C2314yes—
305C2×C4×Dic43C2312yes—
306C2×C4×Dic43C23116yes—
307C42×D43C2311yescharacteristic
308C42×D43C2311yescharacteristic
309C42×D43C2312yes—
310C42×D43C2312yes—
311C42×D43C2311yescharacteristic
312C42×D43C2311yescharacteristic
313C42×D43C2312yes—
314C42×D43C2314yes—
315C42×D43C2314yes—
316C42×D43C2312yes—
317C42×D43C2312yes—
318C42×D43C2314yes—
319C2×#41×C43C2311yescharacteristic
320C2×#41×C43C2318yes—
321C22×D4×C43C2312yes—
322C22×D4×C43C2314yes—
323C4⋊Q8×C43C2312yes—
324#127×C43C2314yes—
325#127×C43C2312yes—
326#127×C43C2312yes—
327#127×C43C2314yes—
328#125×C43C2312yes—
329#124×C43C2318yes—
330#124×C43C2314yes—
331#123×C43C23116yes—
332C22⋊Q8×C43C2314yes—
333#121×C43C2318yes—
334#121×C43C2318yes—
335#121×C43C23116yes—
336#120×C43C2318yes—
337C4×Q8×C43C2312yes—
338C4×Q8×C43C2314yes—
339C4×D4×C43C2314yes—
340C4×D4×C43C2312yes—
341C4×D4×C43C2318yes—
342C4×D4×C43C2318yes—
343C4×D4×C43C2318yes—
344#117×C43C2311yescharacteristic
345#117×C43C2312yes—
346#117×C43C2312yes—
347C2×C22⋊C4×C43C2318yes—
348C2×C42×C43C2311yescharacteristic
349C2×C42×C43C2312yes—
350C24×C43C2414yes—
351C23×D43C2412yes—
352C23×D43C2411yescharacteristic
353#41×C43—24no—
354#41×C43—416no—
355C2×Q8×C43C2411yescharacteristic
356C2×Q8×C43C2414yes—
357C2×D4×C43—28no—
358C2×D4×C43—48no—
359C2×D4×C43C2412yes—
360C2×D4×C43C2414yes—
361C2×D4×C43C2414yes—
362C2×D4×C43C2411yescharacteristic
363C2×D4×C43C2418yes—
364C2×D4×C43C24116yes—
365C2×D4×C43C2418yes—
366C22×C4×C43C2412yes—
367C22×C4×C43C2414yes—
368C22×C4×C43C2412yes—
369C22×C4×C43C24116yes—
370C22×C4×C43C2411yescharacteristic
371C2×C22⋊D43—216no—
372C2×C22⋊D43C2418yes—
373C2×C22⋊D43C2412yes—
374C2×C22⋊D43C2412yes—
375C2×C22⋊D43C2418yes—
376C2×C22⋊D43C2412yes—
377C2×C22⋊D43C24116yes—
378C22×Dic43—216no—
379C22×Dic43C2418yes—
380C22×Dic43C2412yes—
381C22×Dic43C2414yes—
382C22×Dic43C2418yes—
383C22×Dic43C2412yes—
384C22×Dic43C2414yes—
385C22×Dic43C24116yes—
386C22×Dic43C2411yescharacteristic
387#10621902—24no—
388Q8×D43—24no—
389Q8×D43—48no—
390#10621900—28no—
391#10621900—24no—
392#10621900—216no—
393#10621900—216no—
394#10621900—216no—
395#10621900—216no—
396#10621900—416no—
397D4×D43—24no—
398D4×D43—28no—
399#10621898—24no—
400#10621898—28no—
401C2×D172C2412yes—
402C2×D172C2411yescharacteristic
403C2×C4×D43—28no—
404C2×C4×D43—48no—
405C2×C4×D43—44no—
406C2×C4×D43#4118yescomplemented
407C2×C4×D43C2412yes—
408C2×C4×D43C2412yes—
409C2×C4×D43C2412yes—
410C2×C4×D43C2412yes—
411C2×C4×D43C2412yes—
412C2×C4×D43C2414yes—
413C2×C4×D43C2414yes—
414C2×C4×D43C2412yes—
415C2×C4×D43C2412yes—
416C2×C4×D43C2414yes—
417C2×C4×D43C2418yes—
418C2×C4×D43C2411yescharacteristic
419C2×C4×D43C2411yescharacteristic
420C2×C4×D43C2411yescharacteristic
421C2×C4×D43C2411yescharacteristic
422C2×Dic86—28no—
423C2×Dic86C2412yes—
424C2×Dic86C2414yes—
425C2×Dic86C2411yescharacteristic
426C2×Dic86C2414yes—
427C2×Dic86C2414yes—
428C2×Dic86C2418yes—
429C4⋊C4×C43C2412yes—
430C4⋊C4×C43C2414yes—
431C4⋊C4×C43C2414yes—
432C4⋊C4×C43C2414yes—
433C4⋊C4×C43C2418yes—
434C22⋊C4×C43C2412yes—
435C22⋊C4×C43C2414yes—
436C22⋊C4×C43C24116yes—
437C22⋊C4×C43C2414yes—
438C22⋊C4×C43C24116yes—
439C42×C43C2411yescharacteristic
440C42×C43C2412yes—
441C42×C43C2411yescharacteristic
442C42×C43C2414yes—
443C42×C43C2412yes—
444C42×C43C2414yes—
445C22⋊Dic43C2412yes—
446C22⋊Dic43C2414yes—
447C22⋊Dic43C2414yes—
448C22⋊Dic43C24116yes—
449C22⋊Dic43C24116yes—
450C22⋊Dic43C24116yes—
451C22⋊Dic43C24116yes—
452C22⋊Dic43C24116yes—
453(C2×D43)⋊C4C2414yes—
454(C2×D43)⋊C4C2418yes—
455(C2×D43)⋊C4C2414yes—
456(C2×D43)⋊C4C2414yes—
457(C2×D43)⋊C4C24116yes—
458C4⋊Dic43C2412yes—
459C4⋊Dic43C2414yes—
460C4⋊Dic43C2414yes—
461C4⋊Dic43C2414yes—
462C4⋊Dic43C2418yes—
463C4⋊Dic43C2418yes—
464C4⋊Dic43C2418yes—
465C4⋊Dic43C24116yes—
466Dic43⋊C4C2414yes—
467Dic43⋊C4C2418yes—
468Dic43⋊C4C2418yes—
469Dic43⋊C4C2414yes—
470Dic43⋊C4C2414yes—
471Dic43⋊C4C2418yes—
472Dic43⋊C4C2418yes—
473Dic43⋊C4C24116yes—
474Dic43⋊C4C24116yes—
475Dic43⋊C4C24116yes—
476C4×Dic43C2412yes—
477C4×Dic43C2411yescharacteristic
478C4×Dic43C2414yes—
479C4×Dic43C2414yes—
480C4×Dic43C2412yes—
481C4×Dic43C2412yes—
482C4×Dic43C2411yescharacteristic
483C4×Dic43C2414yes—
484C4×Dic43C2412yes—
485C4×Dic43C2412yes—
486C4×Dic43C2414yes—
487C4×Dic43C2412yes—
488C4×Dic43C2418yes—
489C4×Dic43C2414yes—
490C4×Dic43C24116yes—
491C4×Dic43C24116yes—
492C23×C43—28no—
493C23×C43—48no—
494C23×C43C2512yes—
495C23×C43C2518yes—
496C23×C43C2511yescharacteristic
497C22×D43—24no—
498C22×D43—42no—
499C22×D43—44no—
500C22×D43C2×#4114yes—
501C22×D43C2512yes—
502C22×D43C2511yescharacteristic
503C22×D43C2511yescharacteristic
504Q8×C43—22no—
505Q8×C43—28no—
506D4×C43—24no—
507D4×C43—22no—
508D4×C43—28no—
509D4×C43—28no—
510D4×C43—216no—
511D4×C43—48no—
512D4×C43—416no—
513C2×C4×C43—24no—
514C2×C4×C43—24no—
515C2×C4×C43—28no—
516C2×C4×C43—416no—
517C2×C4×C43C2×#4114yes—
518C2×C4×C43C2514yes—
519C2×C4×C43C2518yes—
520C2×C4×C43C2512yes—
521C2×C4×C43C2512yes—
522C2×C4×C43C2511yescharacteristic
523C2×C4×C43C2511yescharacteristic
524C2×C4×C43C2512yes—
525C22⋊D43—24no—
526C22⋊D43—24no—
527C22⋊D43—216no—
528C22⋊D43—216no—
529C22⋊D43—24no—
530C22⋊D43—416no—
531C2×Dic43—28no—
532C2×Dic43—24no—
533C2×Dic43—216no—
534C2×Dic43—216no—
535C2×Dic43—42no—
536C2×Dic43—44no—
537C2×Dic43—416no—
538C2×Dic43C2×#4114yes—
539C2×Dic43C2514yes—
540C2×Dic43C2512yes—
541C2×Dic43C2518yes—
542C2×Dic43C2518yes—
543C2×Dic43C2512yes—
544C2×Dic43C2512yes—
545C2×Dic43C2511yescharacteristic
546C2×Dic43C2511yescharacteristic
547D172—24no—
548D172—22no—
549C4×D43—24no—
550C4×D43—24no—
551C4×D43—24no—
552C4×D43—28no—
553C4×D43—24no—
554C4×D43—24no—
555C4×D43—42no—
556C4×D43—44no—
557C4×D43—42no—
558C4×D43—44no—
559C4×D43—48no—
560C4×D43C2×#4114yes—
561C4×D43C2×#4114yes—
562C4×D43C2×#4114yes—
563C4×D43C2×#4114yes—
564Dic86—28no—
565Dic86—28no—
566Dic86—22no—
567Dic86—28no—
568Dic86—24no—
569Dic86—48no—
570#62815—431nomaximal, Sylow
571C22×C43—22no—
572C22×C43—22no—
573C22×C43—28no—
574C22×C43—24no—
575C22×C43—216no—
576C22×C43—88no—
577C22×C43C22×#4112yes—
578C22×C43C2611yescharacteristic
579C2×D43—22no—
580C2×D43—22no—
581C2×D43—22no—
582C2×D43—24no—
583C2×D43—44no—
584C2×D43—48no—
585C2×D43C22×#4112yes—
586C2×D43C22×#4112yes—
587C4×C43—22no—
588C4×C43—28no—
589C4×C43—24no—
590C4×C43—22no—
591C4×C43C22×#4112yes—
592C4×C43C22×#4112yes—
593C4×C43#58514yes—
594Dic43—22no—
595Dic43—28no—
596Dic43—28no—
597Dic43—22no—
598Dic43—22no—
599Dic43—24no—
600Dic43C22×#4112yes—
601Dic43C22×#4112yes—
602#3512—434no—
603#3511—434no—
604#3510—432no—
605#3510—432no—
606#3509—431no—
607#3509—431no—
608#3508—431no—
609#3508D4311yescharacteristic, complemented
610#3507—434no—
611#3506—434no—
612#3505—438no—
613#3480—434no—
614#3480—434no—
615#3475—438no—
616#3455—434no—
617#3449—432no—
618#3444—434no—
619C2×#533—431no—
620C2×#532—431no—
621#3428—432no—
622C2×C4×#41—431no—
623C2×C43—22no—
624C2×C43—42no—
625C2×C43—48no—
626C2×C43C23×#4111yescharacteristic
627C2×C43C2×#58512yes—
628D43—22no—
629D43—22no—
630D43—42no—
631C22×#41—431no—
632C22×#41—432no—
633#559—438no—
634#559—434no—
635#559—438no—
636#559C2×D4314yescomplemented
637#557—434no—
638#557—434no—
639#556—438no—
640#556—438no—
641#556—434no—
642#556—434no—
643#556—438no—
644#555—438no—
645#554—438no—
646#553—4316no—
647#553—4316no—
648#553—438no—
649#553—4316no—
650#553—438no—
651#552—4316no—
652#552—438no—
653#552—438no—
654#551—4316no—
655#551—4316no—
656#550—434no—
657#550C2×D4314yescomplemented
658#548—438no—
659#548—438no—
660#547—438no—
661#546—438no—
662#546C2×D4318yescomplemented
663#542—438no—
664#542—438no—
665#541—434no—
666#541—434no—
667#540—434no—
668#540C2×D4314yescomplemented
669#539—4316no—
670#538—4316no—
671#537—438no—
672#536—432no—
673#536—434no—
674#536—432no—
675#535—432no—
676#535—434no—
677#535C2×D4312yes—
678#534—438no—
679#533—432no—
680#533—434no—
681#533—432no—
682#533—434no—
683#533—434no—
684#533—432no—
685#533—431no—
686#533—434no—
687#533C2×D4311yescharacteristic, complemented
688#532—432no—
689#532—432no—
690#532—434no—
691#532—434no—
692#532—432no—
693#532—432no—
694#532—434no—
695#532—434no—
696#532—434no—
697#532C2×D4314yescomplemented
698C2×C4⋊Q8—432no—
699C2×C4⋊Q8—431no—
700C2×#127C2×D4311yescharacteristic, complemented
701#529—438no—
702#529—438no—
703#529—4316no—
704#529—438no—
705#529—438no—
706#529—4316no—
707#529—438no—
708#529—438no—
709C2×#125—432no—
710C2×#124—432no—
711#525—438no—
712#525—438no—
713#525—438no—
714#525—438no—
715C2×C22⋊Q8—434no—
716C2×#121—434no—
717#520—438no—
718#520—438no—
719#519—432no—
720#519—432no—
721#518—432no—
722#518—438no—
723#518C2×D4312yescomplemented
724C4×#41—431no—
725C4×#41—438no—
726C4×#41—432no—
727C4×#41—434no—
728C4×#41—432no—
729C4×#41—438no—
730C4×#41—438no—
731C4×#41—438no—
732C4×#41—431no—
733C4×#41—432no—
734C4×#41—431no—
735C4×#41—432no—
736C4×#41C2×D4311yescharacteristic
737C2×C4×Q8—432no—
738C2×C4×Q8—434no—
739C2×C4×D4—434no—
740C2×C4×D4—434no—
741C2×C4×D4—432no—
742C2×#117—431no—
743C2×#117—432no—
744C2×#117—432no—
745C2×#117—438no—
746C22×C42—431no—
747C22×C42—432no—
748C43#6281511yescharacteristic, complemented, Sylow
749C2×#41—431no—
750C2×#41—432no—
751C2×#41—434no—
752C2×#41—431no—
753C2×#41—434no—
754C2×#41—434no—
755C2×#41—434no—
756C2×#41—438no—
757C2×#41—431no—
758C2×#41—432no—
759C2×#41—8616no—
760C2×#41—868no—
761C2×#41C22×D4311yescharacteristic
762C2×#41C22×D4318yes—
763C22×Q8—431no—
764C22×Q8—434no—
765C22×Q8—432no—
766C22×D4—434no—
767C22×D4—432no—
768C22×D4—431no—
769C22×D4C22×D4312yes—
770C22×D4C22×D4314yes—
771C23×C4—431no—
772C23×C4—434no—
773C23×C4—432no—
774C23×C4—432no—
775C23×C4—434no—
776C4⋊Q8—434no—
777C4⋊Q8—434no—
778C4⋊Q8—434no—
779C4⋊Q8—434no—
780C4⋊Q8—432no—
781C4⋊Q8—432no—
782C4⋊Q8—432no—
783C4⋊Q8—434no—
784C4⋊Q8—434no—
785C4⋊Q8C22×D4312yes—
786#127—434no—
787#127C22×D4312yes—
788#127C22×D4312yes—
789#127C22×D4314yes—
790#127C22×D4314yes—
791#126—4316no—
792#126—4316no—
793#126—4316no—
794#126—4316no—
795#126—4316no—
796#126—4316no—
797#125—434no—
798#125—438no—
799#125—438no—
800#125—4316no—
801#125—4316no—
802#125—432no—
803#125—438no—
804#125C22×D4312yes—
805#124—434no—
806#124—434no—
807#124—438no—
808#124—438no—
809#124—4316no—
810#124—434no—
811#124—434no—
812#124—4316no—
813#124—434no—
814#124C22×D4318yes—
815#124C22×D4314yes—
816#123—4316no—
817#123—438no—
818#123—4316no—
819#123—4316no—
820#123—4316no—
821#123—4316no—
822#123—4316no—
823#123—438no—
824#123C22×D43116yes—
825C22⋊Q8—434no—
826C22⋊Q8—438no—
827C22⋊Q8—434no—
828C22⋊Q8—438no—
829C22⋊Q8—438no—
830C22⋊Q8—4316no—
831C22⋊Q8—434no—
832C22⋊Q8—438no—
833C22⋊Q8—438no—
834C22⋊Q8—438no—
835C22⋊Q8—4316no—
836C22⋊Q8—4316no—
837C22⋊Q8C22×D4314yes—
838#121—438no—
839#121—438no—
840#121—438no—
841#121—438no—
842#121—438no—
843#121—438no—
844#121—4316no—
845#121—4316no—
846#121—4316no—
847#121—4316no—
848#121C22×D4318yes—
849#121C22×D4318yes—
850#121C22×D43116yes—
851#120—438no—
852#120—4316no—
853#120C22×D4318yes—
854C4×Q8—434no—
855C4×Q8—432no—
856C4×Q8—438no—
857C4×Q8—434no—
858C4×Q8—434no—
859C4×Q8—432no—
860C4×Q8—438no—
861C4×Q8—438no—
862C4×Q8—438no—
863C4×Q8—434no—
864C4×Q8—432no—
865C4×Q8—434no—
866C4×Q8—438no—
867C4×Q8—438no—
868C4×Q8—438no—
869C4×Q8—438no—
870C4×Q8C22×D4312yes—
871C4×Q8C22×D4314yes—
872C4×D4—438no—
873C4×D4—434no—
874C4×D4—432no—
875C4×D4—438no—
876C4×D4—438no—
877C4×D4—438no—
878C4×D4—438no—
879C4×D4—438no—
880C4×D4—4316no—
881C4×D4—4316no—
882C4×D4—438no—
883C4×D4—434no—
884C4×D4—434no—
885C4×D4—434no—
886C4×D4—4316no—
887C4×D4—4316no—
888C4×D4—4316no—
889C4×D4—434no—
890C4×D4—432no—
891C4×D4—434no—
892C4×D4—434no—
893C4×D4—434no—
894C4×D4—4316no—
895C4×D4—4316no—
896C4×D4—4316no—
897C4×D4—434no—
898C4×D4—432no—
899C4×D4C22×D4314yes—
900C4×D4C22×D4312yes—
901C4×D4C22×D4318yes—
902C4×D4C22×D4318yes—
903C4×D4C22×D4318yes—
904#117—431no—
905#117—432no—
906#117—432no—
907#117—438no—
908#117—4316no—
909#117—432no—
910#117—434no—
911#117—434no—
912#117—438no—
913#117—432no—
914#117—434no—
915#117—4316no—
916#117—434no—
917#117—438no—
918#117—438no—
919#117—4316no—
920#117—4316no—
921#117—432no—
922#117—432no—
923#117—432no—
924#117—434no—
925#117C22×D4311yescharacteristic
926#117C22×D4312yes—
927#117C22×D4312yes—
928C2×C4⋊C4—4316no—
929C2×C4⋊C4—434no—
930C2×C4⋊C4—432no—
931C2×C4⋊C4—434no—
932C2×C4⋊C4—434no—
933C2×C4⋊C4—438no—
934C2×C4⋊C4—434no—
935C2×C22⋊C4—438no—
936C2×C22⋊C4—438no—
937C2×C22⋊C4—432no—
938C2×C22⋊C4—434no—
939C2×C22⋊C4—434no—
940C2×C22⋊C4C22×D4318yes—
941C2×C42—4316no—
942C2×C42—432no—
943C2×C42—434no—
944C2×C42—431no—
945C2×C42—432no—
946C2×C42—432no—
947C2×C42—431no—
948C2×C42—434no—
949C2×C42—434no—
950C2×C42—432no—
951C2×C42—432no—
952C2×C42—434no—
953C2×C42—431no—
954C2×C42—432no—
955C2×C42—431no—
956C2×C42—432no—
957C2×C42—431no—
958C2×C42C22×D4311yescharacteristic
959C2×C42C22×D4312yes—
960C24—431no—
961C24—432no—
962C24C23×D4314yes—
963#41—24no—
964#41—416no—
965#41—868no—
966#41—868no—
967#41—8616no—
968#41—8616no—
969#41—8616no—
970#41—8616no—
971#41—864no—
972#41—864no—
973#41—864no—
974#41—17216no—
975C2×Q8—432no—
976C2×Q8—434no—
977C2×Q8—434no—
978C2×Q8—431no—
979C2×Q8—434no—
980C2×Q8—438no—
981C2×Q8—864no—
982C2×Q8—868no—
983C2×Q8—1728no—
984C2×Q8C23×D4314yes—
985C2×Q8C23×D4311yescharacteristic
986C2×D4—28no—
987C2×D4—48no—
988C2×D4—432no—
989C2×D4—438no—
990C2×D4—432no—
991C2×D4—432no—
992C2×D4—438no—
993C2×D4—4316no—
994C2×D4—432no—
995C2×D4—431no—
996C2×D4—864no—
997C2×D4—868no—
998C2×D4—8616no—
999C2×D4C23×D4318yes—
1000C2×D4C23×D4312yes—
1001C2×D4C23×D4314yes—
1002C2×D4C23×D4311yescharacteristic
1003C2×D4C23×D4314yes—
1004C2×D4C23×D43116yes—
1005C2×D4C23×D4318yes—
1006C22×C4—431no—
1007C22×C4—438no—
1008C22×C4—431no—
1009C22×C4—431no—
1010C22×C4—431no—
1011C22×C4—431no—
1012C22×C4—432no—
1013C22×C4—438no—
1014C22×C4—434no—
1015C22×C4—438no—
1016C22×C4—432no—
1017C22×C4—434no—
1018C22×C4—4316no—
1019C22×C4—432no—
1020C22×C4—432no—
1021C22×C4—432no—
1022C22×C4—432no—
1023C22×C4—434no—
1024C22×C4—432no—
1025C22×C4—434no—
1026C22×C4—432no—
1027C22×C4—432no—
1028C22×C4—434no—
1029C22×C4—438no—
1030C22×C4—868no—
1031C22×C4—8616no—
1032C22×C4—1724no—
1033C22×C4—1728no—
1034C22×C4C23×D4312yes—
1035C22×C4C23×D4314yes—
1036C22×C4C23×D4312yes—
1037C22×C4C23×D43116yes—
1038C22×C4C23×D4311yescharacteristic
1039C4⋊C4—434no—
1040C4⋊C4—438no—
1041C4⋊C4—432no—
1042C4⋊C4—434no—
1043C4⋊C4—438no—
1044C4⋊C4—434no—
1045C4⋊C4—434no—
1046C4⋊C4—434no—
1047C4⋊C4—4316no—
1048C4⋊C4—438no—
1049C4⋊C4—4316no—
1050C4⋊C4—438no—
1051C4⋊C4—434no—
1052C4⋊C4—438no—
1053C4⋊C4—438no—
1054C4⋊C4—438no—
1055C4⋊C4—4316no—
1056C4⋊C4—4316no—
1057C4⋊C4C23×D4314yes—
1058C4⋊C4C23×D4312yes—
1059C4⋊C4C23×D4314yes—
1060C4⋊C4C23×D4314yes—
1061C4⋊C4C23×D4318yes—
1062C22⋊C4—432no—
1063C22⋊C4—434no—
1064C22⋊C4—4316no—
1065C22⋊C4—4316no—
1066C22⋊C4—434no—
1067C22⋊C4—4316no—
1068C22⋊C4—4316no—
1069C22⋊C4—4316no—
1070C22⋊C4—434no—
1071C22⋊C4—438no—
1072C22⋊C4—434no—
1073C22⋊C4—434no—
1074C22⋊C4—4316no—
1075C22⋊C4C23×D4312yes—
1076C22⋊C4C23×D4314yes—
1077C22⋊C4C23×D4314yes—
1078C22⋊C4C23×D43116yes—
1079C22⋊C4C23×D43116yes—
1080C42—434no—
1081C42—432no—
1082C42—431no—
1083C42—432no—
1084C42—438no—
1085C42—432no—
1086C42—434no—
1087C42—434no—
1088C42—431no—
1089C42—432no—
1090C42—432no—
1091C42—434no—
1092C42—432no—
1093C42—4316no—
1094C42—4316no—
1095C42—434no—
1096C42C23×D4311yescharacteristic
1097C42C23×D4312yes—
1098C42C23×D4311yescharacteristic
1099C42C23×D4314yes—
1100C42C23×D4312yes—
1101C42C23×D4314yes—
1102C23—28no—
1103C23—48no—
1104C23—431no—
1105C23—431no—
1106C23—434no—
1107C23—432no—
1108C23—864no—
1109C23—1722no—
1110C23—1724no—
1111C23C24×D4312yes—
1112C23C24×D4318yes—
1113C23C24×D4311yescharacteristic
1114Q8—22no—
1115Q8—28no—
1116Q8—864no—
1117Q8—868no—
1118Q8—862no—
1119Q8—868no—
1120Q8—868no—
1121Q8—1728no—
1122D4—24no—
1123D4—28no—
1124D4—28no—
1125D4—22no—
1126D4—216no—
1127D4—48no—
1128D4—416no—
1129D4—864no—
1130D4—864no—
1131D4—864no—
1132D4—8616no—
1133D4—8616no—
1134D4—864no—
1135D4—862no—
1136D4—17216no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—28no—
1140C2×C4—416no—
1141C2×C4—434no—
1142C2×C4—431no—
1143C2×C4—431no—
1144C2×C4—434no—
1145C2×C4—434no—
1146C2×C4—434no—
1147C2×C4—434no—
1148C2×C4—434no—
1149C2×C4—432no—
1150C2×C4—432no—
1151C2×C4—432no—
1152C2×C4—438no—
1153C2×C4—438no—
1154C2×C4—864no—
1155C2×C4—864no—
1156C2×C4—864no—
1157C2×C4—8616no—
1158C2×C4—8616no—
1159C2×C4—868no—
1160C2×C4—864no—
1161C2×C4—864no—
1162C2×C4—864no—
1163C2×C4—868no—
1164C2×C4—1724no—
1165C2×C4—1724no—
1166C2×C4—1722no—
1167C2×C4—1722no—
1168C2×C4—1728no—
1169C2×C4—1724no—
1170C2×C4—1722no—
1171C2×C4—17216no—
1172C2×C4#41×D4314yes—
1173C2×C4C24×D4314yes—
1174C2×C4C24×D4318yes—
1175C2×C4C24×D4312yes—
1176C2×C4C24×D4312yes—
1177C2×C4C24×D4311yescharacteristic
1178C2×C4C24×D4311yescharacteristic
1179C2×C4C24×D4312yes—
1180C22—22no—
1181C22—22no—
1182C22—28no—
1183C22—24no—
1184C22—216no—
1185C22—88no—
1186C22—432no—
1187C22—432no—
1188C22—862no—
1189C22—862no—
1190C22—862no—
1191C22—864no—
1192C22—1724no—
1193C22—1728no—
1194C22C2×#41×D4312yes—
1195C22C25×D4311yescharacteristic
1196C4—22no—
1197C4—24no—
1198C4—22no—
1199C4—28no—
1200C4—432no—
1201C4—432no—
1202C4—862no—
1203C4—868no—
1204C4—862no—
1205C4—864no—
1206C4—862no—
1207C4—868no—
1208C4C2×#41×D4312yes—
1209C4C2×#41×D4312yes—
1210C4#1458373414yes—
1211C2—22no—
1212C2—48no—
1213C2—42no—
1214C2—862no—
1215C2—862no—
1216C2—1722no—
1217C2C22×#41×D4311yescharacteristic
1218C2C2×#1458373412yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3508C2
hypercenter#3508D43
hypocenterC43#62815
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3508

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19148514C2semidirect
2. #19148496C2semidirect
3. #19148490C2semidirect
4. #19148486C2semidirect
5. #19148482C2semidirect
6. #19148481C2semidirect
7. #19148469C2semidirect
8. #19148452C2semidirect
9. #19148439C2semidirect
10. #19148422C2semidirect
11. #19148194C2semidirect
12. #19148191C2semidirect
13. #19148146C2semidirect
14. #19147979C2semidirect
15. #19147926C2semidirect
16. #19147890C2semidirect
17. #533×D43C2semidirect
18. C2×#14583447C2semidirect
19. #19147793C2semidirect
20. C4×#41×D43C2semidirect
21. C43×#3508C2semidirect
24. #14583635C22semidirect
25. #14583635C22semidirect
26. #14583632C22semidirect
27. #14583628C22semidirect
28. #14583627C22semidirect
29. #14583622C22semidirect
30. #14583619C22semidirect
31. #14583619C22semidirect
32. #14583618C22semidirect
33. #14583618C22semidirect
34. #14583613C22semidirect
35. #14583608C22semidirect
36. #14583599C22semidirect
37. #14583596C22semidirect
38. #14583596C22semidirect
39. #14583594C22semidirect
40. #14583592C22semidirect
41. #14583591C22semidirect
42. #14583589C22semidirect
43. #14583586C22semidirect
44. #14583580C22semidirect
45. #14583575C22semidirect
46. #14583569C22semidirect
47. #14583557C22semidirect
48. #14583556C22semidirect
49. #14583548C22semidirect
50. #14583543C22semidirect
51. #14583516C22semidirect
52. #14583514C22semidirect
53. #14583512C22semidirect
54. #14583511C22semidirect
55. #14583503C22semidirect
56. #14583492C22semidirect
57. #14583481C22semidirect
58. #14583478C22semidirect
61. #14583469C22semidirect
63. #14583462C22semidirect
65. #14583456C22semidirect
66. #14583456C22semidirect
67. #14583455C22semidirect
68. #14583454C22semidirect
69. #14583454C22semidirect
70. #14583453C22semidirect
71. #14583452C22semidirect
72. #14583451C22semidirect
73. #14583448C22semidirect
77. #14583447C22semidirect
78. #14583447C22semidirect
79. #14583447C22semidirect
80. #14583447C22semidirect
81. #14583447C22semidirect
82. C2×#13063325C22semidirect
83. C4⋊Q8×D43C22semidirect
84. #14583431C22semidirect
85. #14583431C22semidirect
86. #14583430C22semidirect
87. #14583430C22semidirect
88. #14583430C22semidirect
89. #14583428C22semidirect
90. #14583428C22semidirect
91. #14583426C22semidirect
92. #125×D43C22semidirect
93. C2×#13063312C22semidirect
94. #14583409C22semidirect
95. #14583409C22semidirect
96. #14583406C22semidirect
100. #14583378C22semidirect
101. #14583378C22semidirect
102. #14583376C22semidirect
103. #14583376C22semidirect
104. #14583374C22semidirect
107. #41×Dic43C22semidirect
108. C4×#10621902C22semidirect
110. C4×#10621898C22semidirect
112. #14583367C22semidirect
114. C4×#10621900C22semidirect
115. C4×#10621900C22semidirect
116. C4×#10621900C22semidirect
117. C4×#10621900C22semidirect
118. C4×Q8×D43C22semidirect
119. C4×Q8×D43C22semidirect
120. C2×D4×Dic43C22semidirect
122. C4×D4×D43C22semidirect
123. C2×#13063281C22semidirect
126. #117×D43C22semidirect
128. C2×C42×D43C22semidirect
129. C43×#559C22semidirect
130. C43×#550C22semidirect
131. C43×#546C22semidirect
132. C43×#540C22semidirect
134. C43×#533C22semidirect
135. C43×#532C22semidirect
136. C2×#127×C43C22semidirect
137. C43×#518C22semidirect
406. C2×C4×D43#41semidirect
609. #3508D43semidirect
636. #559C2×D43semidirect
657. #550C2×D43semidirect
662. #546C2×D43semidirect
668. #540C2×D43semidirect
687. #533C2×D43semidirect
697. #532C2×D43semidirect
700. C2×#127C2×D43semidirect
723. #518C2×D43semidirect
748. C43#62815semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191485142
#191484962
#191484902
#191484862
#191484822
#191484812
#191484692
#191484522
#191484392
#191484222
#191481942
#191481912
#191481462
#191479792
#191479262
#191478902
#533×D432
C2×#145834472
#191477932
C4×#41×D432
C43×#35082
#6281543